What is Solved Examples Based On Power 1?

Find the power of a locomotive drawing a train weighing 1600 kN up an incline 1 in 100 at a steady speed of 54 kmph, the frictional resistance being 5 N/kN.

While the train is ascending the incline, the steam is shut off. Find how far it will move before coming to rest, assuming that the resistance to motion remains the same.

Solution

Figure (a) shows the system of forces acting on the locomotive while moving up the incline with steady speed.

v = 54 kmph

= 54 × 1000 / 60 × 60 = 15 m/sec

F = 5 × 1600 = 8000 N = 8.0 kN

Σ Forces parallel to plane = 0

P – F – W sin θ = 0

P = 8 + 1600 × 1/100

= 24 kN [Since q is small, sin q = tan q = 1/100.]

Power of the locomotive = Work done by P per second

= P × Distance moved per second

= Pv

= 24 × 15 = 360 kN-m/sec

Power = 360 kW

After the steam is put off, let the train move a distance s metres and come to rest.

Initial velocity, u = 15 m/sec

Final velocity, v = 0

Figure (b) shows the system of forces acting in this case. Writing down work- energy equation, we get

- (F + W sin θ)s = 11600/29.81 (0 - 152)

(8 + 1600 X 1/100)s = 1/2 X 1600/9.81 X 225

∴ s = 764.52 m

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